Deduction 6 - What can we say about the angles of a parallelogram?

Transcript

Deduction 6 What can we say about the angles of a parallelogram?Let’s consider the Parallelogram we just constructed Let’s find the other angles of parallelogram ABCD Since AD and BC are parallel Taking AB as transversal Sum of interior angles on same side of transversal is 180° ∠ DAB + ∠ CBA = 180° 30° + ∠ CBA = 180° ∠ CBA = 180° – 30° ∠ CBA = 150° Also, Since AB and CD are parallel Taking AD as transversal Sum of interior angles on same side of transversal is 180° ∠ DAB + ∠ ADC = 180° 30° + ∠ ADC = 180° ∠ ADC = 180° – 30° ∠ ADC = 150° Now, Applying Angle Sum Property in Parallelogram ABCD Sum of angles = 360° ∠ A + ∠ B + ∠ C + ∠ D = 360° 30° + 150° + ∠ C + 150° = 360° 330° + ∠ C = 360° ∠ C = 360° – 330° ∠ C = 30° Thus, we note that Opposite angles of parallelogram are equal Sum of Adjacent angles of parallelogram is 180°